創造性を培う数学的問題のタイプに関する研究

抄録

The study of creativity and creative thinking in educational/psychological research has been highly fashionable since the 1950s. Recently, in Japan, it is emphasized that mathematics education should contribute to help students develop their creativity and creative thinking in school mathematics for the 21st century. We can find some important suggestions for fostering students' creativity out from the results of research done within the subject of school mathematics, though we do not have enough information about such mathematical problems that could be used in teaching and learning of mathematics suited for students to develop their creativity and creative thinking. The purpose of this research is to identify and make clear such mathematical problems that could be used in teaching and learning of school mathematics in order to foster students' creativity and creative thinking from the view point of mathematics education. To do it, we first summarize main results of the research on creativity and creative thinking in the area of psychology. Second we think about our conception of students' creativity that should be fostered in mathematics education. Finally, basing on these considerations, we identify five different types of mathematical problem as follows and show two illuminating sample problems to each type with the key-question in each type of mathematical problem. Type 1: Mathematical problem of encouraging students to find as many mathematical patterns/relations as possible in a given mathematical situation Type 2: Mathematical problem of encouraging students to think as many ways as possible to a given mathematical task Type 3: Mathematical problem of encouraging students to have and represent as many images as possible in a given mathematical situation Type 4: Mathematical problem of encouraging students to understand different ideas represented by the given different mathematical representations Type 5: Mathematical problem of encouraging students to pose new and extended mathematical problems by changing some attributes of a given mathematical problem All types are related to divergent thinking in general, but each type has its own characteristic feature from the mathematical view point. The framework of these types could be useful and helpful for us in mathematics education.